Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets
A formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and cross-correlation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of L2(R), some results on the...
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2019-07-01
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| Series: | Arab Journal of Mathematical Sciences |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1319516618301531 |
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doaj-84e054d52f864f19b2e2b653699f40b02021-05-02T22:11:46ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662019-07-01252169179Some results on vanishing moments of wavelet packets, convolution and cross-correlation of waveletsA.M. Jarrah0Nikhil Khanna1Department of Mathematics, Yarmouk University, Irbid, Jordan; Correspondence to: Academic Affairs, Tafila Technical University, Jordan.Department of Mathematics, University of Delhi, Delhi, IndiaA formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and cross-correlation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of L2(R), some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given. Keywords: Wavelet packets, Hilbert transformation, Moments, Wavelet packets, Mathematics Subject Classification: 42C40, 44A15, 44A60, 65T60http://www.sciencedirect.com/science/article/pii/S1319516618301531 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A.M. Jarrah Nikhil Khanna |
| spellingShingle |
A.M. Jarrah Nikhil Khanna Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets Arab Journal of Mathematical Sciences |
| author_facet |
A.M. Jarrah Nikhil Khanna |
| author_sort |
A.M. Jarrah |
| title |
Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets |
| title_short |
Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets |
| title_full |
Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets |
| title_fullStr |
Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets |
| title_full_unstemmed |
Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets |
| title_sort |
some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets |
| publisher |
Emerald Publishing |
| series |
Arab Journal of Mathematical Sciences |
| issn |
1319-5166 |
| publishDate |
2019-07-01 |
| description |
A formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and cross-correlation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of L2(R), some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given. Keywords: Wavelet packets, Hilbert transformation, Moments, Wavelet packets, Mathematics Subject Classification: 42C40, 44A15, 44A60, 65T60 |
| url |
http://www.sciencedirect.com/science/article/pii/S1319516618301531 |
| work_keys_str_mv |
AT amjarrah someresultsonvanishingmomentsofwaveletpacketsconvolutionandcrosscorrelationofwavelets AT nikhilkhanna someresultsonvanishingmomentsofwaveletpacketsconvolutionandcrosscorrelationofwavelets |
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